- Email: [email protected]
Modeling of the thermodynamic properties of the mixtures: Prediction of the position of azeotropes for binary mixtures
Fluid Phase Equilibria 379 (2014) 120–127
Contents lists available at ScienceDirect
Fluid Phase Equilibria journal homepage: www.elsevier.com/locate/fluid
Modeling of the thermodynamic properties of the mixtures: Prediction of the position of azeotropes for binary mixtures Saida Fedali ∗ , Hakim Madani, Cherif Bougriou Laboratoire d’étude des systèmes Energétiques Industriels, Département de Mécanique, Faculté de Technologie, Université Hadj Lakhdar Batna, Algeria
a r t i c l e
i n f o
Article history: Received 28 February 2014 Received in revised form 6 July 2014 Accepted 16 July 2014 Available online 24 July 2014 Keywords: Azeotrope Binary mixture Vapor–liquid equilibrium Equation of state
a b s t r a c t In this paper, we present a novel approach to predict the location of azeotropes for binary mixtures by two methods: from the experimental data and the thermodynamic model. The model composed of the Peng–Robinson equation of state, the Mathias–Copeman alpha function, the Wong–Sandler mixing rules involving the NRTL model. The binary mixtures of refrigerants selected are: propane (R290) + 1,1,1,2-tetrafluoroethane (R134a) [1], propane (R290) + difluoromethane (R32) [2] and hexafluoroethane (R116) + ethane (R170) [3], hexafluoroethane (R116) + carbon dioxide (R744) [4] and hexafluoroethane (R116) + propane (R290) [5], to be favorable to the environment with a null ODP (ozone depletion potential) and a low GWP (global warming). The results prove that there is an agreement between the predicted values and the experimental data and the relative error does not exceed 2.76% for the molar fraction and 3.23% for the pressure. The presented methods are able to predict the azeotropic position and the performances of the models change from one mixture to another. © 2014 Published by Elsevier B.V.
1. Introduction Our world is always changing; we need to preserve the global environment. The phenomenon of the impoverishment of the ozone layer and the climatic reheating are the two problems very discussed of these last years. To solve these problems, various protocols, of with those Montreal Protocol 1987 (ozone depletion) and Kyoto Protocol 1997 (Global Warming: (effective on Feb. 16, 2005)/EU F-gas Regulation (Directive 2006/40/EC)) specified the refrigerant regulation. In the field of the refrigeration, many researches are undertaken to find new refrigeration mixtures with minimal environmental impact (ozone depletion and global warming). In industry, the presence of azeotropes in mixtures has value is interesting because they behave very nearly as pure materials and when it is a mixture of chemicals in solution and not a compound where those chemicals exhibit strong molecular bonds that are not easily broken. The mixtures show azeotropic behavior and calculation of such property is particularly important in designing of azeotropic distillation.
Many numbers of researches in our group [6–14] have been studied. Our main objective is to develop a new and sample method for the prediction of the position of azeotrope in the binary mixtures. In this study, we presented a new approach for determination of azeotropy directly from the experimental data and theoretically from the thermodynamic model. We studied five binary systems of refrigerants: propane + R134a, propane + R32, R116 + R170, R116 + R744 and R116 + propane. 2. Mathematical modeling Recently, many methods and approaches have been used to predict the location of azeotropes for vapor–liquid equilibrium of binary mixtures. We have developed a model for the position of azeotropic mixture refrigerant. We applied the method which is based on experimental data for calculation and prediction of azeotropes and then we confirmed our method by using a thermodynamic model. 2.1. From the experimental data
∗ Corresponding author. E-mail addresses: saida [email protected] (S. Fedali), madani [email protected] (H. Madani). http://dx.doi.org/10.1016/j.fluid.2014.07.018 0378-3812/© 2014 Published by Elsevier B.V.
The azeotropic position is determined for each system (xaz : azeotropic composition, Paz : azeotropic pressure). With the experimental values, plotting the value of relative volatility (˛) according to the molar fraction of the most volatile pure substance, and then
S. Fedali et al. / Fluid Phase Equilibria 379 (2014) 120–127
121
Table 1 Critical parameters from dataa Compound
Pc (MPa)
Tc (K)
R290 R134a R32 R116 R170 R744
4.192 4.064 5.753 2.941 4.872 7.286
369.83 374.30 351.60 292.80 305.32 304.21
a
From [21].
Table 2 Mathias–Copeman coefficients. Coefficients
C1
C2
C3
R290a R134ab R32c R116d R170e R744f
0.892 0.849 1.034 0.875 0.531 0.704
−1.936 0.006 −1.454 −3.243 −0.062 −0.314
8.815 −0.053 4.038 0.254 0.214 1.890
a b c d e f
Adjusted. [15]. [2]. [16]. [21]. [15].
we equalizing the obtained curve (˛) to 1 (the same principle for the pressure). 2.1.1. Algorithm - For each isotherm, we trace either the relative volatility (˛) according to the molar fraction of the most volatile pure substance x1 , or according to the pressure. - Using the Excel, plotted points either to a curve (trendline) of a second-degree polynomial (or linear) is adjusted. Table 3 Azeotropes preaching. T (K)
Xo
- Equalizing the equation of the curve of tendency to 1. - Solving the obtained equation, where values are obtained xaz and Paz .
2.2. From the thermodynamic model K1
Xe
K1
Possibility of having an azeotrope
R290 + R134a 0.0991 273.15 0.1153 283.15 0.0490 293.15 0.0850 303.15 313.15 0.0505
3.63 3.02 3.70 2.72 2.95
0.9149 0.9445 0.9897 0.9707 0.9293
0.89 0.92 0.98 0.96 0.94
Yes Yes Yes Yes Yes
R290 + R32 0.0430 278.10 0.0080 294.83 0.0270 303.23
5.49 6.13 4.67
0.9750 0.9570 0.9530
0.94 0.94 0.96
Yes Yes Yes
R116 + R170 183.31 0.2547 0.2352 192.63 0.1572 247.63 0.1264 252.80
2.21 2.28 1.81 1.88
0.7874 0.7518 0.7340 0.7432
0.93 0.95 0.96 0.96
Yes Yes Yes Yes
R116 + R744 0.0284 253.29 0.0281 273.27 0.0592 283.24
1.78 1.37 1.16
0.9477 0.9327 0.9732
0.92 0.94 0.98
Yes Yes Yes
0.961 0.946 0.941 0.808 0.569 0.392
1.002 1.003 1.004 1.010 1.056 1.074
No No No No No No
R116 + R290 263.30 0.019 0.020 283.25 0.020 291.22 0.018 296.23 0.029 308.21 0.030 323.10
Fig. 1. Deviation of pressure and vapor-phase composition for R290 + R134a system.
11.470 8.400 7.450 7.060 5.241 4.167
Xo , Xe : the experimental molar fractions of initial and final azeotropes, respectively.
Our thermodynamic model based on a simple correlative scheme that allows one to judge if can be obtained or not Table 4 Experimental and calculated compositions and pressures of the azeotrope at each temperature of R290 + R134a, R290 + R32, R116 + R170 and R116 + R744. T (K)
Xaz(exp)
Xaz(cal)
Paz(exp)
Paz(cal)
R290 + R134a 273.15 283.15 293.15 303.15 313.15 323.15
0.6486 0.6430 0.6358 0.6171 0.5935 0.5914
0.6461 0.6411 0.6306 0.6211 0.6057 0.5964
0.5972 0.7939 1.0603 1.3595 1.7289 2.1318
0.5948 0.7950 1.0582 1.3572 1.7245 2.1291
R290 + R32 278.10 294.83 303.23 313.26
0.6610 06746 0.6838 0.6964
0.6593 0.6748 0.6827 0.6903
1.2193 1.9211 2.3498 2.9903
1.2217 1.9006 2.3517 2.9603
R116 + R170 189.31 192.63 247.63 252.80
0.7027 0.6958 0.6662 0.6630
0.6979 0.6986 0.6674 0.6634
0.1688 0.1937 1.4652 1.7160
0.1634 0.1926 1.4636 1.6902
R116 + R744 253.29 273.27 283.24
0.2051 0.1822 0.1790
0.1996 0.1821 0.1735
2.1640 3.7280 4.7740
2.1796 3.7458 4.8050
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S. Fedali et al. / Fluid Phase Equilibria 379 (2014) 120–127
Fig. 2. Deviation of pressure and vapor-phase composition for R290 + R32 system.
an azeotrope is probable in binary refrigerant mixtures. We have used the Peng Robinson (PR) EoS [17] together with the Mathias–Copeman alpha function (Eqs. (4) and (5)) [18] for accurate representation of the pure component vapor pressures. The critical temperature (Tc ) and critical pressure (Pc ) for each pure component is given in Table 1. P=
RT
v−b
−
a(T ) (v2 + 2vb − v2 )
Fig. 3. Deviation of pressure and vapor-phase composition for R116 + R170 system.
where c1 , c2 and c3 are adjustable parameters (see Table 2).- The Wong–Sandler (WS) mixing rules are chosen here from the good representation of vapor–liquid equilibria [19]
b=
(1) b−
with a = 0.457240
x x (b − a/RT ) j i j x (a /bi )/RT + gE (T, P = ∞, x)/CRT ) i i i i
1−(
a a xi xj b − = RT RT i
R2 Tc2 Pc
(2)
RTc b = 0.07780 Pc
(3)
Mathias–Copeman alpha function 2
3 2
˛(T ) = [1 + c1 (1 − Tr0.5 ) + c2 (1 − Tr0.5 ) + c3 (1 − Tr0.5 ) ]
(4)
If T > Tc ˛(T ) = [1 + c1 (1 − Tr0.5 )]
a b− RT
(5)
ij
1 = 2
a b− RT
(7)
ij
j
a + b− RT i
j
n
G x j=1 ji ji j n G x k=1 ki k
+
n j=1
xj Gij
n
G x k=1 ki k
n x G k=1 k kj kj ij − n
Table 5 The equations of the curve of tendency of the binary mixtures Paz = f(T) and Xaz = f(T).
R134a + R290 R290 + R32 R116 + R170 R116 + R744
(1 − kij )
(8)
where kij is an adjustable binary interaction parameter and C is a numerical constant which depends on the EoS.- The component activity parameters of binary mixture system are calculated with model NRTL (non-random two liquids) [20] Lni =
2
(6)
Paz = f(T)
Xaz = f(T)
Paz = 0.0002T2 − 0.0638T + 5.8777 Paz = 0.0005T2 − 0.2358T + 29.3971 Paz = 0.0004T2 − 0.1420T + 13.5902 Paz = 0.0009T2 − 0.4113T + 46.6887
Xaz = −0.00003T2 + 0.018T − 1.882 Xaz = 0.00001T2 − 0.005T + 1.279 Xaz = 0.000007T2 − 0.003T + 1.145 Xaz = 0.0000004T2 − 0.001T + 0.452
G x k=1 ki k
(9)
S. Fedali et al. / Fluid Phase Equilibria 379 (2014) 120–127
123
Fig. 6. Azeotropic composition and pressure versus temperature for R290 + R32 system. Fig. 4. Deviation of pressure and vapor-phase composition for R116 + R744 system.
Fig. 5. Azeotropic composition and pressure versus temperature for R290 + R134a system.
Fig. 7. Azeotropic composition and pressure versus temperature for R116 + R170 system.
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S. Fedali et al. / Fluid Phase Equilibria 379 (2014) 120–127
Fig. 8. VLE for the system R290 + R134a at different temperatures: () 273.15 K, () 283.15 K, (䊉) 293.15 K, () 303.15 K, (♦) 313.15 K, () 323.15 K.
Fig. 9. VLE for the system R290 + R32 at different temperatures: () 278.10 K, () 294.83 K, (䊉) 303.23 K, () 313.66 K.
where the model parameters Cij and Gij are defined as follows: Cji =
ij
Gij = exp −˛ji
(10)
RT
ji
(11)
RT
The excess Gibbs energy model chosen is the NRTL [17] Table 6 Values of the binary parameters at each temperature for R290 + R134a. T (K)
12
21
273.15 283.15 293.15 303.15 313.15 323.15
4144 5305 6332 5858 3948 2113
3953 4553 5500 3874 2999 2563
gE = K12 −0.0001 −0.1146 −0.2322 −0.1164 0.0626 0.1903
xj exp(−˛ji (ji /RT )) xi ji i
(12)
xk exp(−˛ki (ki /RT ))
j k
where ˛ji , ji and ij are adjustable parameters. It is recommended [15] to use ˛ij = 0.3 for systems like the current one. Where ii = jj = 0 and ˛ii = 0.
S. Fedali et al. / Fluid Phase Equilibria 379 (2014) 120–127
125
Fig. 10. VLE for the system R116 + R170 at different temperatures: (a) () 189.31 K, () 192.63 K, (b) () 247.63 K, (♦) 252.80 K.
3. Results and discussions
3.1. Prediction of azeotropes
Predicting the composition for an azeotropic is of key importance in fluid-phase equilibrium of the refrigerant mixture is very important before it can be tested for its refrigeration characteristics.
First the value of the partition coefficient K1 = x1 /y1 of the most volatile pure substance is calculated for each isotherm. Azeotropic behavior of the mixture is predicted using the mole fractions and not pressure.
Table 7 Values of the binary parameters at each temperature for R290 + R32.
Table 8 Values of the binary parameters at each temperature for R116 + R170.
T (K)
12
21
K12
T (K)
12
278.10 294.83 303.23 313.66
4019 4160 3951 1566
3731 4045 3793 3341
0.1827 0.1394 0.1657 0.3325
189.31 192.63 247.63 252.80
3385 3396 3401 3000
21 237 −110 794 786
K12 0.2301 0.2915 0.1500 0.1800
126
S. Fedali et al. / Fluid Phase Equilibria 379 (2014) 120–127
Fig. 11. VLE for the system R116 + R744 at different temperatures: () 253.29 K, () 273.27 K, (䊉) 283.24 K.
Table 3 shows the first four mixtures which have azeotropic mixture except the last mixture (R116 + R290). The compositions of the vapor and liquid phases are the same when we are in the presence of an azeotrope.
Comparison between the experimental values measured to those of the values computed of azeotropic compositions and pressures by the following relations:Molar fraction xaz c/o
xaz = 3.2. Determination of azeotropes from the experimental data From the experimental data, we will determine the position of the azeotropes (xaz : molar fraction, Paz : pressure in MPa) for each mixture, the algorithm is clarified before. The values of the molar fraction and the azeotrope pressure calculated of the data experimental ones, and those obtained from the model are illustrated in Table 4.
xaz(exp) − xaz(cal) Xaz(exp)
∗ 100
(13)
∗ 100
(14)
Pressure Pazeo c/o
Paz =
Paz(exp) − Paz(cal) Paz(exp)
The relative error values plotted in Figs. 1–4 indicate that this method gives good predictions of the azeotrope location and the relative error does not exceed 2.76% for the molar fraction and 3.23% for the pressure.
Fig. 12. VLE for the system R116 + R290 at different temperatures: () 263.30 K, () 283.20 K, (䊉) 291.22 K, () 296.23 K, (♦) 308.21 K, () 323.19 K.
S. Fedali et al. / Fluid Phase Equilibria 379 (2014) 120–127 Table 9 Values of the binary parameters at each temperature for R116 + R744.
List of symbols
T (K)
12
21
K12
253.29 273.27 283.24
362 324 287
3977 4073 3650
0.2171 0.1917 0.2177
Table 10 Values of the binary parameters at each temperature for R116 + R290. T (K) 263.30 283.25 291.22 296.23 308.21 323.19
12 1891 1783 921 596 608 795
127
21
K12
3292 3194 3497 3691 3806 3749
0.1301 0.1383 0.1910 0.2073 0.1930 0.1756
Collected figures.
To widening our study more in a range of temperature (see Table 4), the molar fractions of azeotropes and those pressures in function to temperature have been traced (Figs. 5-7). We can have the value of the molar fraction of azeotrope where the pressure according to the temperature of the systems quoted in Table 5. 3.3. Determination of the azeotropes from a thermodynamic model The vapor pressures of the binary mixtures are presented in the publications [1–5]. The effectiveness of our method, we will justify further, where by using a very robust thermodynamic model which gave its consistency in a large number of articles published (paragraph 2). The experimental and calculated data PTxy are illustrated in Figs. 8–12 according to the system studied. Figs. 8 to 10 present an azeotrope between 0.6 and 0.8 for the systems (R290 + R134a, R290 + R32 and R116 + R170) and between 0.0 and 0.3 in the system R116 + R290 (Fig. 11). This azeotrope is a homogeneous azeotrope at maximum pressure (for isothermal). Where the composition of the liquid phase and the composition of the vapor phase are identical, the mixture is the same process as a pure substance. R116 + R290 (Fig. 12) does not present an azeotrope, the system presents a quasi-azeotrope, then disappeared above the critical point of R116, which in maid agreements with the experimental values. The adjusted NRTL ( 12 and 21 ) parameters for the Wong–Sandler mixing rules (K12 ) obtained at each temperature are given in Tables 6–10. 4. Conclusion In this study, isothermal VLE data have been determined for propane + 1,1,1,2-tetrafluoroethane at T = 278.15–313.15 K and propane + difluoromethane at T = 278.10–303.23 K and hexafluoroethane + ethane at T = 189.31–252.80 K and hexafluoroethane + carbone at T = 253.29–283.24 K and hexafluoroethane + propane at T = 263.20–223.19 K using two methods. The results have been correlated with the Peng–Robinson equation of state using the Mathias–Copeman alpha function and Wong–Sandler mixing rules with the NRTL GE model. The approach provided reasonably good fits to the values measured. The obtained results of the present model for the binary mixtures prove that the present model works well for these binary mixtures. Therefore, this model can be applicable to the other binary refrigerant mixtures.
a b c C g kij K1 N P R T x y
parameter of the equation of state [energy parameter (J m3 mol−2 )] parameter of the equation of state [molar co-volume parameter (m3 mol−1 )] Mathias–Copeman coefficient numerical constant equal to −0.62323 molar Gibbs energy (J mol−1 ) binary interaction parameter partition coefficient number of experimental points pressure (MPa) gas constant (J mol−1 K−1 ) temperature (K) liquid mole fraction vapor mole fraction
Greek letters alpha function (Eqs. (4) and (5)) ˛ ˛ji non-randomness NRTL model parameter (Eq. (8)) ij NRTL model binary interaction parameter (Eq. (9)) (J mol−1 ) ji NRTL model binary interaction parameter (Eqs. (8)–(11)) (J mol−1 ) ∞ infinite pressure reference state Superscript excess property E Subscripts azeotropic property az critical property C cal calculated property end e exp experimental property molecular species i, j r reduced most volatile pure substance 1 2 less volatile pure substance References [1] J.S. Lim, J.Y. Park, J.W. Kang, B.G. Lee, Fluid Phase Equilibria 243 (2006) 57–63. [2] C. Coquelet, A. Chareton, A. Valtz, A.B. Ahmed, D. Richon, J. Chem. Eng. Data 48 (2003) 317–323. [3] C. Coquelet, Al. Valtz, D. Richon, Fluid Phase Equilibria 232 (2005) 44–49. [4] A. Valtz, C. Coquelet, D. Richon, Fluid Phase Equilibria 258 (2007) 179–185. [5] D. Ramjugernath, A. Valtz, C. Coquelet, D. Richon, J. Chem. Eng. Data 54 (2009) 1292–1296. [6] A.S. Telat, J.S. Rowlinson, Chem. Eng. Sci. 28 (1973) 529–538. [7] J. Gmehling, J. Menke, J. Krafczyk, K. Fischer, Fluid Phase Equilibria 103 (1995) 51–76. [8] A.V. Trotsenko, Fluid Phase Equilibria 127 (1997) 123–127. [9] H. Segura, J. Wisniak, P.G. Toledo, A. Mejıa, Fluid Phase Equilibria 166 (1999) 141–162. [10] R.M.B. Alves, F.H. Quina, C.A.O. Nascimento, Comput. Chem. Eng. 27 (2003) 1755–1759. [11] N. Aslam, A.K. Sunol, Fluid Phase Equilibria 224 (2004) 97–109. [12] S. Artemenko, V. Mazur, Int. J. Refrig. 30 (2007) 831–839. [13] X. Yingjie, Y. Jia, Y. Ping, L. Haoran, H. Shijun, Thermodynamics and chemical engineering data, Chin. J. Chem. Eng. 18 (2010) 455–461. [14] V.Z. Shahabadi, M. Lotfizadeh, A.R.A. Gandomani, M.M. Papari, J. Mol. Liquids 188 (2013) 222–229. [15] H. Madani, A. Valtz, C. Coquelet, A.H. Meniai, D. Richon, Int. J. Refrig. 32 (2009) 1396–1402. [16] H. Madani, Doctoral Thesis, University of Batna, 2010. [17] D.Y. Peng, D.B. Robinson, Ind. Eng. Chem. Fundam. 15 (1976) 59–64. [18] P.M. Mathias, T.W. Copeman, Fluid Phase Equilibria 13 (1983) 91–108. [19] D.S.H. Wong, S.I. Sandler, AIChE J. 38 (1992) 671–680. [20] H. Renon, J.M. Prausnitz, AIChE J. 14 (1968) 135–144. [21] Dortmund Data Bank (DDB) version 2009, DDBST Software and Separation Technology GmbH, Oldenburg. Germany.
Contents lists available at ScienceDirect
Fluid Phase Equilibria journal homepage: www.elsevier.com/locate/fluid
Modeling of the thermodynamic properties of the mixtures: Prediction of the position of azeotropes for binary mixtures Saida Fedali ∗ , Hakim Madani, Cherif Bougriou Laboratoire d’étude des systèmes Energétiques Industriels, Département de Mécanique, Faculté de Technologie, Université Hadj Lakhdar Batna, Algeria
a r t i c l e
i n f o
Article history: Received 28 February 2014 Received in revised form 6 July 2014 Accepted 16 July 2014 Available online 24 July 2014 Keywords: Azeotrope Binary mixture Vapor–liquid equilibrium Equation of state
a b s t r a c t In this paper, we present a novel approach to predict the location of azeotropes for binary mixtures by two methods: from the experimental data and the thermodynamic model. The model composed of the Peng–Robinson equation of state, the Mathias–Copeman alpha function, the Wong–Sandler mixing rules involving the NRTL model. The binary mixtures of refrigerants selected are: propane (R290) + 1,1,1,2-tetrafluoroethane (R134a) [1], propane (R290) + difluoromethane (R32) [2] and hexafluoroethane (R116) + ethane (R170) [3], hexafluoroethane (R116) + carbon dioxide (R744) [4] and hexafluoroethane (R116) + propane (R290) [5], to be favorable to the environment with a null ODP (ozone depletion potential) and a low GWP (global warming). The results prove that there is an agreement between the predicted values and the experimental data and the relative error does not exceed 2.76% for the molar fraction and 3.23% for the pressure. The presented methods are able to predict the azeotropic position and the performances of the models change from one mixture to another. © 2014 Published by Elsevier B.V.
1. Introduction Our world is always changing; we need to preserve the global environment. The phenomenon of the impoverishment of the ozone layer and the climatic reheating are the two problems very discussed of these last years. To solve these problems, various protocols, of with those Montreal Protocol 1987 (ozone depletion) and Kyoto Protocol 1997 (Global Warming: (effective on Feb. 16, 2005)/EU F-gas Regulation (Directive 2006/40/EC)) specified the refrigerant regulation. In the field of the refrigeration, many researches are undertaken to find new refrigeration mixtures with minimal environmental impact (ozone depletion and global warming). In industry, the presence of azeotropes in mixtures has value is interesting because they behave very nearly as pure materials and when it is a mixture of chemicals in solution and not a compound where those chemicals exhibit strong molecular bonds that are not easily broken. The mixtures show azeotropic behavior and calculation of such property is particularly important in designing of azeotropic distillation.
Many numbers of researches in our group [6–14] have been studied. Our main objective is to develop a new and sample method for the prediction of the position of azeotrope in the binary mixtures. In this study, we presented a new approach for determination of azeotropy directly from the experimental data and theoretically from the thermodynamic model. We studied five binary systems of refrigerants: propane + R134a, propane + R32, R116 + R170, R116 + R744 and R116 + propane. 2. Mathematical modeling Recently, many methods and approaches have been used to predict the location of azeotropes for vapor–liquid equilibrium of binary mixtures. We have developed a model for the position of azeotropic mixture refrigerant. We applied the method which is based on experimental data for calculation and prediction of azeotropes and then we confirmed our method by using a thermodynamic model. 2.1. From the experimental data
∗ Corresponding author. E-mail addresses: saida [email protected] (S. Fedali), madani [email protected] (H. Madani). http://dx.doi.org/10.1016/j.fluid.2014.07.018 0378-3812/© 2014 Published by Elsevier B.V.
The azeotropic position is determined for each system (xaz : azeotropic composition, Paz : azeotropic pressure). With the experimental values, plotting the value of relative volatility (˛) according to the molar fraction of the most volatile pure substance, and then
S. Fedali et al. / Fluid Phase Equilibria 379 (2014) 120–127
121
Table 1 Critical parameters from dataa Compound
Pc (MPa)
Tc (K)
R290 R134a R32 R116 R170 R744
4.192 4.064 5.753 2.941 4.872 7.286
369.83 374.30 351.60 292.80 305.32 304.21
a
From [21].
Table 2 Mathias–Copeman coefficients. Coefficients
C1
C2
C3
R290a R134ab R32c R116d R170e R744f
0.892 0.849 1.034 0.875 0.531 0.704
−1.936 0.006 −1.454 −3.243 −0.062 −0.314
8.815 −0.053 4.038 0.254 0.214 1.890
a b c d e f
Adjusted. [15]. [2]. [16]. [21]. [15].
we equalizing the obtained curve (˛) to 1 (the same principle for the pressure). 2.1.1. Algorithm - For each isotherm, we trace either the relative volatility (˛) according to the molar fraction of the most volatile pure substance x1 , or according to the pressure. - Using the Excel, plotted points either to a curve (trendline) of a second-degree polynomial (or linear) is adjusted. Table 3 Azeotropes preaching. T (K)
Xo
- Equalizing the equation of the curve of tendency to 1. - Solving the obtained equation, where values are obtained xaz and Paz .
2.2. From the thermodynamic model K1
Xe
K1
Possibility of having an azeotrope
R290 + R134a 0.0991 273.15 0.1153 283.15 0.0490 293.15 0.0850 303.15 313.15 0.0505
3.63 3.02 3.70 2.72 2.95
0.9149 0.9445 0.9897 0.9707 0.9293
0.89 0.92 0.98 0.96 0.94
Yes Yes Yes Yes Yes
R290 + R32 0.0430 278.10 0.0080 294.83 0.0270 303.23
5.49 6.13 4.67
0.9750 0.9570 0.9530
0.94 0.94 0.96
Yes Yes Yes
R116 + R170 183.31 0.2547 0.2352 192.63 0.1572 247.63 0.1264 252.80
2.21 2.28 1.81 1.88
0.7874 0.7518 0.7340 0.7432
0.93 0.95 0.96 0.96
Yes Yes Yes Yes
R116 + R744 0.0284 253.29 0.0281 273.27 0.0592 283.24
1.78 1.37 1.16
0.9477 0.9327 0.9732
0.92 0.94 0.98
Yes Yes Yes
0.961 0.946 0.941 0.808 0.569 0.392
1.002 1.003 1.004 1.010 1.056 1.074
No No No No No No
R116 + R290 263.30 0.019 0.020 283.25 0.020 291.22 0.018 296.23 0.029 308.21 0.030 323.10
Fig. 1. Deviation of pressure and vapor-phase composition for R290 + R134a system.
11.470 8.400 7.450 7.060 5.241 4.167
Xo , Xe : the experimental molar fractions of initial and final azeotropes, respectively.
Our thermodynamic model based on a simple correlative scheme that allows one to judge if can be obtained or not Table 4 Experimental and calculated compositions and pressures of the azeotrope at each temperature of R290 + R134a, R290 + R32, R116 + R170 and R116 + R744. T (K)
Xaz(exp)
Xaz(cal)
Paz(exp)
Paz(cal)
R290 + R134a 273.15 283.15 293.15 303.15 313.15 323.15
0.6486 0.6430 0.6358 0.6171 0.5935 0.5914
0.6461 0.6411 0.6306 0.6211 0.6057 0.5964
0.5972 0.7939 1.0603 1.3595 1.7289 2.1318
0.5948 0.7950 1.0582 1.3572 1.7245 2.1291
R290 + R32 278.10 294.83 303.23 313.26
0.6610 06746 0.6838 0.6964
0.6593 0.6748 0.6827 0.6903
1.2193 1.9211 2.3498 2.9903
1.2217 1.9006 2.3517 2.9603
R116 + R170 189.31 192.63 247.63 252.80
0.7027 0.6958 0.6662 0.6630
0.6979 0.6986 0.6674 0.6634
0.1688 0.1937 1.4652 1.7160
0.1634 0.1926 1.4636 1.6902
R116 + R744 253.29 273.27 283.24
0.2051 0.1822 0.1790
0.1996 0.1821 0.1735
2.1640 3.7280 4.7740
2.1796 3.7458 4.8050
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Fig. 2. Deviation of pressure and vapor-phase composition for R290 + R32 system.
an azeotrope is probable in binary refrigerant mixtures. We have used the Peng Robinson (PR) EoS [17] together with the Mathias–Copeman alpha function (Eqs. (4) and (5)) [18] for accurate representation of the pure component vapor pressures. The critical temperature (Tc ) and critical pressure (Pc ) for each pure component is given in Table 1. P=
RT
v−b
−
a(T ) (v2 + 2vb − v2 )
Fig. 3. Deviation of pressure and vapor-phase composition for R116 + R170 system.
where c1 , c2 and c3 are adjustable parameters (see Table 2).- The Wong–Sandler (WS) mixing rules are chosen here from the good representation of vapor–liquid equilibria [19]
b=
(1) b−
with a = 0.457240
x x (b − a/RT ) j i j x (a /bi )/RT + gE (T, P = ∞, x)/CRT ) i i i i
1−(
a a xi xj b − = RT RT i
R2 Tc2 Pc
(2)
RTc b = 0.07780 Pc
(3)
Mathias–Copeman alpha function 2
3 2
˛(T ) = [1 + c1 (1 − Tr0.5 ) + c2 (1 − Tr0.5 ) + c3 (1 − Tr0.5 ) ]
(4)
If T > Tc ˛(T ) = [1 + c1 (1 − Tr0.5 )]
a b− RT
(5)
ij
1 = 2
a b− RT
(7)
ij
j
a + b− RT i
j
n
G x j=1 ji ji j n G x k=1 ki k
+
n j=1
xj Gij
n
G x k=1 ki k
n x G k=1 k kj kj ij − n
Table 5 The equations of the curve of tendency of the binary mixtures Paz = f(T) and Xaz = f(T).
R134a + R290 R290 + R32 R116 + R170 R116 + R744
(1 − kij )
(8)
where kij is an adjustable binary interaction parameter and C is a numerical constant which depends on the EoS.- The component activity parameters of binary mixture system are calculated with model NRTL (non-random two liquids) [20] Lni =
2
(6)
Paz = f(T)
Xaz = f(T)
Paz = 0.0002T2 − 0.0638T + 5.8777 Paz = 0.0005T2 − 0.2358T + 29.3971 Paz = 0.0004T2 − 0.1420T + 13.5902 Paz = 0.0009T2 − 0.4113T + 46.6887
Xaz = −0.00003T2 + 0.018T − 1.882 Xaz = 0.00001T2 − 0.005T + 1.279 Xaz = 0.000007T2 − 0.003T + 1.145 Xaz = 0.0000004T2 − 0.001T + 0.452
G x k=1 ki k
(9)
S. Fedali et al. / Fluid Phase Equilibria 379 (2014) 120–127
123
Fig. 6. Azeotropic composition and pressure versus temperature for R290 + R32 system. Fig. 4. Deviation of pressure and vapor-phase composition for R116 + R744 system.
Fig. 5. Azeotropic composition and pressure versus temperature for R290 + R134a system.
Fig. 7. Azeotropic composition and pressure versus temperature for R116 + R170 system.
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S. Fedali et al. / Fluid Phase Equilibria 379 (2014) 120–127
Fig. 8. VLE for the system R290 + R134a at different temperatures: () 273.15 K, () 283.15 K, (䊉) 293.15 K, () 303.15 K, (♦) 313.15 K, () 323.15 K.
Fig. 9. VLE for the system R290 + R32 at different temperatures: () 278.10 K, () 294.83 K, (䊉) 303.23 K, () 313.66 K.
where the model parameters Cij and Gij are defined as follows: Cji =
ij
Gij = exp −˛ji
(10)
RT
ji
(11)
RT
The excess Gibbs energy model chosen is the NRTL [17] Table 6 Values of the binary parameters at each temperature for R290 + R134a. T (K)
12
21
273.15 283.15 293.15 303.15 313.15 323.15
4144 5305 6332 5858 3948 2113
3953 4553 5500 3874 2999 2563
gE = K12 −0.0001 −0.1146 −0.2322 −0.1164 0.0626 0.1903
xj exp(−˛ji (ji /RT )) xi ji i
(12)
xk exp(−˛ki (ki /RT ))
j k
where ˛ji , ji and ij are adjustable parameters. It is recommended [15] to use ˛ij = 0.3 for systems like the current one. Where ii = jj = 0 and ˛ii = 0.
S. Fedali et al. / Fluid Phase Equilibria 379 (2014) 120–127
125
Fig. 10. VLE for the system R116 + R170 at different temperatures: (a) () 189.31 K, () 192.63 K, (b) () 247.63 K, (♦) 252.80 K.
3. Results and discussions
3.1. Prediction of azeotropes
Predicting the composition for an azeotropic is of key importance in fluid-phase equilibrium of the refrigerant mixture is very important before it can be tested for its refrigeration characteristics.
First the value of the partition coefficient K1 = x1 /y1 of the most volatile pure substance is calculated for each isotherm. Azeotropic behavior of the mixture is predicted using the mole fractions and not pressure.
Table 7 Values of the binary parameters at each temperature for R290 + R32.
Table 8 Values of the binary parameters at each temperature for R116 + R170.
T (K)
12
21
K12
T (K)
12
278.10 294.83 303.23 313.66
4019 4160 3951 1566
3731 4045 3793 3341
0.1827 0.1394 0.1657 0.3325
189.31 192.63 247.63 252.80
3385 3396 3401 3000
21 237 −110 794 786
K12 0.2301 0.2915 0.1500 0.1800
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S. Fedali et al. / Fluid Phase Equilibria 379 (2014) 120–127
Fig. 11. VLE for the system R116 + R744 at different temperatures: () 253.29 K, () 273.27 K, (䊉) 283.24 K.
Table 3 shows the first four mixtures which have azeotropic mixture except the last mixture (R116 + R290). The compositions of the vapor and liquid phases are the same when we are in the presence of an azeotrope.
Comparison between the experimental values measured to those of the values computed of azeotropic compositions and pressures by the following relations:Molar fraction xaz c/o
xaz = 3.2. Determination of azeotropes from the experimental data From the experimental data, we will determine the position of the azeotropes (xaz : molar fraction, Paz : pressure in MPa) for each mixture, the algorithm is clarified before. The values of the molar fraction and the azeotrope pressure calculated of the data experimental ones, and those obtained from the model are illustrated in Table 4.
xaz(exp) − xaz(cal) Xaz(exp)
∗ 100
(13)
∗ 100
(14)
Pressure Pazeo c/o
Paz =
Paz(exp) − Paz(cal) Paz(exp)
The relative error values plotted in Figs. 1–4 indicate that this method gives good predictions of the azeotrope location and the relative error does not exceed 2.76% for the molar fraction and 3.23% for the pressure.
Fig. 12. VLE for the system R116 + R290 at different temperatures: () 263.30 K, () 283.20 K, (䊉) 291.22 K, () 296.23 K, (♦) 308.21 K, () 323.19 K.
S. Fedali et al. / Fluid Phase Equilibria 379 (2014) 120–127 Table 9 Values of the binary parameters at each temperature for R116 + R744.
List of symbols
T (K)
12
21
K12
253.29 273.27 283.24
362 324 287
3977 4073 3650
0.2171 0.1917 0.2177
Table 10 Values of the binary parameters at each temperature for R116 + R290. T (K) 263.30 283.25 291.22 296.23 308.21 323.19
12 1891 1783 921 596 608 795
127
21
K12
3292 3194 3497 3691 3806 3749
0.1301 0.1383 0.1910 0.2073 0.1930 0.1756
Collected figures.
To widening our study more in a range of temperature (see Table 4), the molar fractions of azeotropes and those pressures in function to temperature have been traced (Figs. 5-7). We can have the value of the molar fraction of azeotrope where the pressure according to the temperature of the systems quoted in Table 5. 3.3. Determination of the azeotropes from a thermodynamic model The vapor pressures of the binary mixtures are presented in the publications [1–5]. The effectiveness of our method, we will justify further, where by using a very robust thermodynamic model which gave its consistency in a large number of articles published (paragraph 2). The experimental and calculated data PTxy are illustrated in Figs. 8–12 according to the system studied. Figs. 8 to 10 present an azeotrope between 0.6 and 0.8 for the systems (R290 + R134a, R290 + R32 and R116 + R170) and between 0.0 and 0.3 in the system R116 + R290 (Fig. 11). This azeotrope is a homogeneous azeotrope at maximum pressure (for isothermal). Where the composition of the liquid phase and the composition of the vapor phase are identical, the mixture is the same process as a pure substance. R116 + R290 (Fig. 12) does not present an azeotrope, the system presents a quasi-azeotrope, then disappeared above the critical point of R116, which in maid agreements with the experimental values. The adjusted NRTL ( 12 and 21 ) parameters for the Wong–Sandler mixing rules (K12 ) obtained at each temperature are given in Tables 6–10. 4. Conclusion In this study, isothermal VLE data have been determined for propane + 1,1,1,2-tetrafluoroethane at T = 278.15–313.15 K and propane + difluoromethane at T = 278.10–303.23 K and hexafluoroethane + ethane at T = 189.31–252.80 K and hexafluoroethane + carbone at T = 253.29–283.24 K and hexafluoroethane + propane at T = 263.20–223.19 K using two methods. The results have been correlated with the Peng–Robinson equation of state using the Mathias–Copeman alpha function and Wong–Sandler mixing rules with the NRTL GE model. The approach provided reasonably good fits to the values measured. The obtained results of the present model for the binary mixtures prove that the present model works well for these binary mixtures. Therefore, this model can be applicable to the other binary refrigerant mixtures.
a b c C g kij K1 N P R T x y
parameter of the equation of state [energy parameter (J m3 mol−2 )] parameter of the equation of state [molar co-volume parameter (m3 mol−1 )] Mathias–Copeman coefficient numerical constant equal to −0.62323 molar Gibbs energy (J mol−1 ) binary interaction parameter partition coefficient number of experimental points pressure (MPa) gas constant (J mol−1 K−1 ) temperature (K) liquid mole fraction vapor mole fraction
Greek letters alpha function (Eqs. (4) and (5)) ˛ ˛ji non-randomness NRTL model parameter (Eq. (8)) ij NRTL model binary interaction parameter (Eq. (9)) (J mol−1 ) ji NRTL model binary interaction parameter (Eqs. (8)–(11)) (J mol−1 ) ∞ infinite pressure reference state Superscript excess property E Subscripts azeotropic property az critical property C cal calculated property end e exp experimental property molecular species i, j r reduced most volatile pure substance 1 2 less volatile pure substance References [1] J.S. Lim, J.Y. Park, J.W. Kang, B.G. Lee, Fluid Phase Equilibria 243 (2006) 57–63. [2] C. Coquelet, A. Chareton, A. Valtz, A.B. Ahmed, D. Richon, J. Chem. Eng. Data 48 (2003) 317–323. [3] C. Coquelet, Al. Valtz, D. Richon, Fluid Phase Equilibria 232 (2005) 44–49. [4] A. Valtz, C. Coquelet, D. Richon, Fluid Phase Equilibria 258 (2007) 179–185. [5] D. Ramjugernath, A. Valtz, C. Coquelet, D. Richon, J. Chem. Eng. Data 54 (2009) 1292–1296. [6] A.S. Telat, J.S. Rowlinson, Chem. Eng. Sci. 28 (1973) 529–538. [7] J. Gmehling, J. Menke, J. Krafczyk, K. Fischer, Fluid Phase Equilibria 103 (1995) 51–76. [8] A.V. Trotsenko, Fluid Phase Equilibria 127 (1997) 123–127. [9] H. Segura, J. Wisniak, P.G. Toledo, A. Mejıa, Fluid Phase Equilibria 166 (1999) 141–162. [10] R.M.B. Alves, F.H. Quina, C.A.O. Nascimento, Comput. Chem. Eng. 27 (2003) 1755–1759. [11] N. Aslam, A.K. Sunol, Fluid Phase Equilibria 224 (2004) 97–109. [12] S. Artemenko, V. Mazur, Int. J. Refrig. 30 (2007) 831–839. [13] X. Yingjie, Y. Jia, Y. Ping, L. Haoran, H. Shijun, Thermodynamics and chemical engineering data, Chin. J. Chem. Eng. 18 (2010) 455–461. [14] V.Z. Shahabadi, M. Lotfizadeh, A.R.A. Gandomani, M.M. Papari, J. Mol. Liquids 188 (2013) 222–229. [15] H. Madani, A. Valtz, C. Coquelet, A.H. Meniai, D. Richon, Int. J. Refrig. 32 (2009) 1396–1402. [16] H. Madani, Doctoral Thesis, University of Batna, 2010. [17] D.Y. Peng, D.B. Robinson, Ind. Eng. Chem. Fundam. 15 (1976) 59–64. [18] P.M. Mathias, T.W. Copeman, Fluid Phase Equilibria 13 (1983) 91–108. [19] D.S.H. Wong, S.I. Sandler, AIChE J. 38 (1992) 671–680. [20] H. Renon, J.M. Prausnitz, AIChE J. 14 (1968) 135–144. [21] Dortmund Data Bank (DDB) version 2009, DDBST Software and Separation Technology GmbH, Oldenburg. Germany.